Spatially inhomogeneous thermo field dynamics

Non-equilibrium thermo field dynamics is extended to treat spatially inhomogeneous systems. A canonical formalism of thermally dissipative semi-free fields describing spatially inhomogeneous situations is presented. With this formalism, a scheme of perturbative calculations is developed and the "on-shell" renormalization condition is discussed. We illustrate this scheme using a model of particles interacting with impurities and find that the self-consistent renormalization condition gives the kinetic equation for the averaged particle number density as well as the renormalized energy and the dissipative coefficient. It is also shown that this kinetic equation can be reduced to the Boltzmann equation in the gradient expansion approximation.